Question: Simplify the following expression: $ q = \dfrac{-2r}{r + 6} + \dfrac{-7}{4} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{-2r}{r + 6} \times \dfrac{4}{4} = \dfrac{-8r}{4r + 24} $ Multiply the second expression by $\dfrac{r + 6}{r + 6}$ $ \dfrac{-7}{4} \times \dfrac{r + 6}{r + 6} = \dfrac{-7r - 42}{4r + 24} $ Therefore $ q = \dfrac{-8r}{4r + 24} + \dfrac{-7r - 42}{4r + 24} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-8r - 7r - 42}{4r + 24} $ $q = \dfrac{-15r - 42}{4r + 24}$